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Complete intersection

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  1. an algebraic variety V in projective space is a complete intersection if it can be defined by the vanishing of the number of homogeneous polynomials indicated by its codimension

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  2. a term from mathematics

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  3. That is, if the dimension of an algebraic variety of V is m and it lies in projective space Pn, there are homogeneous polynomials in the homogeneous coordinates Xj, with such that on V we have and for no other points of projective space do all the Fi

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  4. Geometrically each Fi separately define a hypersurface Hi

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  5. the intersection of the Hi should be V, no more and no less

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  6. In fact the dimension of the intersection will always be at least m, assuming as usual in algebraic geometry that the scalars form an algebraically closed field, such as the complex numbers

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
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